Moduli space theory for constant mean curvature surfaces

Robert Kusner

University of Massachusetts at Amherst

Brandeis University

Thursday, March 23, 2006

Talk at 4:30 p.m. in 317 Goldsmith Hall

Tea at 4:00 p.m. in 300 Goldsmith Hall

Abstract: Properly embedded constant mean curvature (CMC) surfaces, which model complete noncompact soap bubbles and equilibrium fluid droplets, have a particular asymptotic behavior. This leads to a pair of natural questions: How well do the asymptotic data determine the surface? Can one describe the moduli space of all CMC surfaces with a given (finite) topology, using these asymptotic data as natural parameters? The key to answering these questions, at least in part, is the nondegeneracy of the linearized mean curvature (or second variation of area, or Jacobi) operator. We'll report on recent joint work with K. Grosse-Brauckmann, N. Korevaar, J. Ratzkin and J. Sullivan, where we have found good estimates on the nullity of the Jacobi operator; though we have shown the operator is nondegenerate for a large class of surfaces, many interesting open problems remain.

Home Web page: Alexandru I. Suciu Posted: March 10, 2006
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